Finite Group Databasebeta

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D3×#120×C11⋊C5 #72217543

order10560
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C27

Aliases

direct productD3×#120×C11⋊C5

Splittings

FittingC3×C11×#120 ⋊ C2×C5
HallD3×C11×#120 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×#120
HallC3×C11 ⋊ C2×C5×#120
SylowC11 ⋊ C5×D3×#120
SylowC3 ⋊ C2×#120×C11⋊C5

Subgroups

subgroupG/H
center, FrattiniC22C23×D3×C11⋊C5
commutator, socle, cosocleC22×C3×C11C24×C5
FittingC3×C11×#120C2×C5
hypercenter#120D3×C11⋊C5
hypocenterC3×C11C2×C5×#120
LCSG ▷ C22×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ #120

2648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×#120×AGL(1,𝔽11)
maximal normal subgroup ofD3×#120×AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.